论文标题
大规模拓扑中的小无数枢机主教
Small uncountable cardinals in large-scale topology
论文作者
论文摘要
在本文中，我们有兴趣查找和评估在大规模拓扑中出现的连续体的基本特征，通常是属于某些类别（不差异，不分配的，大的，大，大）或局部有限的粗糙结构的最小粗结构的重量。除了著名的红衣主教$ \ Mathfrak B，\ Mathfrak D，\ Mathfrak C $，我们将遇到两个新的红衣主教$ \Mathsfδ$和$ \ \ Mathsfσ$，该$ $ \ MATHSFσ$定义为$ω$上的最小重量结构的最小重量，该结构不包含离散的子空间，没有分离的设置，并且相应地分开了。我们证明了$ \ max \ {\ Mathfrak b，\ Mathfrak s，\ Mathrm {cov}（\ Mathcal n）\} \ le \ le \ le \mathsfδ\ le \ le \ le \mathsfσ\ le \ le \ le \ le \ le \ mathrm {non}（non}（non}（\ mathcal m），我们不知道costinals $ $ $ σ，\ mathrm {non}（\ mathcal m）$可以在合适的ZFC模型中分开。
In this paper we are interested in finding and evaluating cardinal characteristics of the continuum that appear in large-scale topology, usually as the smallest weights of coarse structures that belong to certain classes (indiscrete, inseparated, large) of finitary or locally finite coarse structures on $ω$. Besides well-known cardinals $\mathfrak b,\mathfrak d,\mathfrak c$ we shall encounter two new cardinals $\mathsf Δ$ and $\mathsf Σ$, defined as the smallest weight of a finitary coarse structure on $ω$ which contains no discrete subspaces and no asymptotically separated sets, respectively. We prove that $\max\{\mathfrak b,\mathfrak s,\mathrm{cov}(\mathcal N)\}\le\mathsf Δ\le\mathsf Σ\le\mathrm{non}(\mathcal M)$, but we do not know if the cardinals $\mathsf Δ,\mathsf Σ,\mathrm{non}(\mathcal M)$ can be separated in suitable models of ZFC.
